One of the nice features of the classic set of pentominoes is that the twelve pieces, each with five unit squares, total to an area of sixty units. Sixty, of course, is evenly divisible by a lot of numbers, and it turns out that the pieces can be used to create a variety of rectangular sizes: 3×20, 4×15, 5×12, and 6×10. This was very handy when I recently decided to build a cabinet of shelves to go into the parlor room of my house.

I wanted a set of shelves to display some of my puzzles and geometric models on, and I wanted the cabinet to span pretty much the whole length of one wall (with the top surface coming in just below the windows of the south wall). Having four possible rectangle sizes to choose from allowed me to use a height/width ratio that fit my needs perfectly.

I ended up going with a 4×15 rectangle and having each square cell measure 7 inches (before having to account for the thickness of the boards). The final cabinet measured 105.75" wide and 28.75" tall, which filled the blank area of the wall exactly as I desired. Here are a couple of pictures of the shelves taken immediately after I set them up:

Sharp-eyed readers will notice that the gap between the bottom of the cabinet and the floor is slightly larger on the left hand side. This is because the parlor used to be an outdoor porch and thus had a sloped floor to allow water runoff. The top of the cabinet is level with the windows above it.

Once installed, I quickly filled the shelves with a bunch of puzzles and geometric models that I have created throughout the years. The following ten minute video gives a brief tour of this bric-a-brac: